Thoughts on games (with probably too much computational complexity) updating every Tuesday and Friday some days during the school year

Friday, September 23, 2011

Game Description: Zuniq

Wow, some good games were suggested by readers two weeks ago! In addition to Nick Bentleydonating Y with Shifts, Marcos Donnantuoni commented about his own impartial game, Zuniq. Ernie and I tried this out on Monday, and we immediately liked playing this! Here's how the game works:

The starting board is a grid of dots, similar to dots and boxes. Each turn, a player connects two adjacent (vertical or horizontal; not diagonal) dots, but not exactly like dots and boxes. If a new line segment closes off a region, no future turns can be made inside that region. Also, no two regions can have the same size. Thus, you can't close off a region if a region of that size already exists.

The suggested starting 8x8 board is a bit large, but we gave it a go. (Video: [7:16]) Afterwards we tried with 3x3 boards, to quickly learn that they are not very interesting. (The first player can always win by being just a little bit smart.)

The 4x4 game is definitely more interesting. (Video of lots of little games. [6:08]) After a few of these games, and later with games played against Patrick and my WittSempeer mentor, Alec, I think I can consistently win going first there. Still, my initial guess is that the game is PSPACE-complete in general.

I feel like there are lots of nice theorems that can be shown about this game. At the same time, I'm not familiar with what sort of theorems are "useful" from a CGT perspective (aside from computational complexity results).

Combinatorial Game Man

artist: Molly Dannaher

What is This?

This blog is devoted to Combinatorial Game Theory! Combinatorial games are two-player games with no randomness, perfect information (no one has any hidden information) and no draws allowed, though sometimes topics stray into other types of games as well.

Please let me know if you are interested in either writing a guest post or suggesting a topic. I would like this to be more reflective of CGT as a whole and not restrict it to my take on things. Additionally, please help me fill out the table of game properties, either by suggesting games or letting me know about results!